X₂₃₇₉

CIR(X₅₃₁)

X₂₃₇₉ = 2nd-Parry-to-ABC similarity image of X₁₆

5, 6, 7 3, 4, 5 Kepler Kimberling

X₂₃₇₉ (CIR(X₅₃₁)) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

Constructed Elements

• Central Lines: {16, 110}, {99, 299}

• Related Centers: X₁₆ (2nd ISODYNAMIC POINT), X₁₁₀ (FOCUS OF KIEPERT PARABOLA), X₉₉ (STEINER POINT), X₂₉₉ (ISOTOMIC CONJUGATE OF 2nd ISOGONIC CENTER)

Trilinears: \(F(u,v,w) : F(v,w,u) : F(w,u,v)\), where F is as indicated just before X₂₃₆₅, and \(u : v : w\) = X₅₃₁.

Barycentrics: \(aF(u,v,w) : bF(v,w,u) : cF(w,u,v)\)

Search Value (6, 9, 13): \(12.413829024897\)

X₂₃₇₉ lies on the circumcircle.

▸ Incident Central Lines5 lines

{13, 476}, {15, 691}, {16, 110}, {99, 299}, {512, 2378}

▸ Functional Relations3 relations

• X₂₃₇₉ = 2nd-Parry-to-ABC similarity image of X₁₆

• X₂₃₇₉ = 3rd-Parry-to-circumsymmedial similarity image of X₁₅

• X₂₃₇₉ = isogonal conjugate of X₅₃₁